Energy density from second shape variations of the von Neumann entropy

Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

doi:10.1103/PhysRevD.98.086013

Title: Energy density from second shape variations of the von Neumann entropy

Authors:: Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

Publication Date:: Wed Oct 10 00:00:00 EDT 2018

Sponsoring Org.:: USDOE

OSTI Identifier:: 1477552

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 8; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Citation Formats


                    Leichenauer, Stefan, Levine, Adam, and Shahbazi-Moghaddam, Arvin. Energy density from second shape variations of the von Neumann entropy.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.086013.

Copy to clipboard


                    Leichenauer, Stefan, Levine, Adam, & Shahbazi-Moghaddam, Arvin. Energy density from second shape variations of the von Neumann entropy.  United States.  https://doi.org/10.1103/PhysRevD.98.086013

Copy to clipboard


                    Leichenauer, Stefan, Levine, Adam, and Shahbazi-Moghaddam, Arvin. Wed .  
"Energy density from second shape variations of the von Neumann entropy".  United States.  https://doi.org/10.1103/PhysRevD.98.086013.

Copy to clipboard


                    
@article{osti_1477552,

  title        = {Energy density from second shape variations of the von Neumann entropy},

  author       = {Leichenauer, Stefan and Levine, Adam and Shahbazi-Moghaddam, Arvin},

  abstractNote = {},

  doi          = {10.1103/PhysRevD.98.086013},

  journal      = {Physical Review D},

  number       = 8,

  volume       = 98,

  place        = {United States},

  year         = {Wed Oct 10 00:00:00 EDT 2018},

  month        = {Wed Oct 10 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.98.086013

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 18 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
journal, January 2015

Engelhardt, Netta; Wall, Aron C.
Journal of High Energy Physics, Vol. 2015, Issue 1
DOI: 10.1007/JHEP01(2015)073

Building up spacetime with quantum entanglement
journal, June 2010

Van Raamsdonk, Mark
General Relativity and Gravitation, Vol. 42, Issue 10
DOI: 10.1007/s10714-010-1034-0

Entanglement Equilibrium and the Einstein Equation
journal, May 2016

Jacobson, Ted
Physical Review Letters, Vol. 116, Issue 20
DOI: 10.1103/PhysRevLett.116.201101

Entropy on a null surface for interacting quantum field theories and the Bousso bound
journal, April 2015

Bousso, Raphael; Casini, Horacio; Fisher, Zachary
Physical Review D, Vol. 91, Issue 8
DOI: 10.1103/PhysRevD.91.084030

Building up Space–Time with Quantum Entanglement
journal, December 2010

Van Raamsdonk, Mark
International Journal of Modern Physics D, Vol. 19, Issue 14
DOI: 10.1142/S0218271810018529

Proof of the generalized second law for rapidly evolving Rindler horizons
journal, December 2010

Wall, Aron C.
Physical Review D, Vol. 82, Issue 12
DOI: 10.1103/PhysRevD.82.124019

Relative entropy and the Bekenstein bound
journal, September 2008

Casini, H.
Classical and Quantum Gravity, Vol. 25, Issue 20
DOI: 10.1088/0264-9381/25/20/205021

Nonlinear gravity from entanglement in conformal field theories
journal, August 2017

Faulkner, Thomas; Haehl, Felix M.; Hijano, Eliot
Journal of High Energy Physics, Vol. 2017, Issue 8
DOI: 10.1007/JHEP08(2017)057

Averaged null energy condition from causality
journal, July 2017

Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)066

Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

Lashkari, Nima; McDermott, Michael B.; Van Raamsdonk, Mark
Journal of High Energy Physics, Vol. 2014, Issue 4
DOI: 10.1007/JHEP04(2014)195

Saturation of the quantum null energy condition in far-from-equilibrium systems
journal, June 2018

Ecker, Christian; Grumiller, Daniel; van der Schee, Wilke
Physical Review D, Vol. 97, Issue 12
DOI: 10.1103/PhysRevD.97.126016

Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
journal, May 2012

Wall, Aron C.
Physical Review D, Vol. 85, Issue 10
DOI: 10.1103/PhysRevD.85.104049

Cool horizons for entangled black holes
journal, August 2013

Maldacena, J.; Susskind, L.
Fortschritte der Physik, Vol. 61, Issue 9
DOI: 10.1002/prop.201300020

Holographic proof of the quantum null energy condition
journal, July 2016

Koeller, Jason; Leichenauer, Stefan
Physical Review D, Vol. 94, Issue 2
DOI: 10.1103/PhysRevD.94.024026

Shape dependence of entanglement entropy in conformal field theories
journal, April 2016

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
Journal of High Energy Physics, Vol. 2016, Issue 4
DOI: 10.1007/JHEP04(2016)088

Some calculable contributions to holographic entanglement entropy
journal, August 2011

Hung, Ling-Yan; Myers, Robert C.; Smolkin, Michael
Journal of High Energy Physics, Vol. 2011, Issue 8
DOI: 10.1007/JHEP08(2011)039

Entanglement density and gravitational thermodynamics
journal, May 2015

Bhattacharya, Jyotirmoy; Hubeny, Veronika E.; Rangamani, Mukund
Physical Review D, Vol. 91, Issue 10
DOI: 10.1103/PhysRevD.91.106009

Local modular Hamiltonians from the quantum null energy condition
journal, March 2018

Koeller, Jason; Leichenauer, Stefan; Levine, Adam
Physical Review D, Vol. 97, Issue 6
DOI: 10.1103/PhysRevD.97.065011

Quantum focusing conjecture
journal, March 2016

Bousso, Raphael; Fisher, Zachary; Leichenauer, Stefan
Physical Review D, Vol. 93, Issue 6
DOI: 10.1103/PhysRevD.93.064044

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Ryu, Shinsei; Takayanagi, Tadashi
Physical Review Letters, Vol. 96, Issue 18
DOI: 10.1103/PhysRevLett.96.181602

Bare Quantum Null Energy Condition
journal, February 2018

Fu, Zicao; Marolf, Donald
Physical Review Letters, Vol. 120, Issue 7
DOI: 10.1103/PhysRevLett.120.071601

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
journal, August 2017

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 36
DOI: 10.1088/1751-8121/aa7eaa

Thermodynamics of Spacetime: The Einstein Equation of State
journal, August 1995

Jacobson, Ted
Physical Review Letters, Vol. 75, Issue 7
DOI: 10.1103/PhysRevLett.75.1260

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)038

Lower Bound on the Energy Density in Classical and Quantum Field Theories
journal, April 2017

Wall, Aron C.
Physical Review Letters, Vol. 118, Issue 15
DOI: 10.1103/PhysRevLett.118.151601

State-dependent divergences in the entanglement entropy
journal, October 2016

Marolf, Donald; Wall, Aron C.
Journal of High Energy Physics, Vol. 2016, Issue 10
DOI: 10.1007/JHEP10(2016)109

A covariant holographic entanglement entropy proposal
journal, July 2007

Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
Journal of High Energy Physics, Vol. 2007, Issue 07
DOI: 10.1088/1126-6708/2007/07/062

Ads/CFT correspondence and symmetry breaking
journal, September 1999

Klebanov, Igor R.; Witten, Edward
Nuclear Physics B, Vol. 556, Issue 1-2
DOI: 10.1016/S0550-3213(99)00387-9

Holographic entanglement entropy for general higher derivative gravity
journal, January 2014

Dong, Xi
Journal of High Energy Physics, Vol. 2014, Issue 1
DOI: 10.1007/JHEP01(2014)044

Violating the quantum focusing conjecture and quantum covariant entropy bound in d ⩾ 5 dimensions
journal, August 2017

Fu, Zicao; Koeller, Jason; Marolf, Donald
Classical and Quantum Gravity, Vol. 34, Issue 17
DOI: 10.1088/1361-6382/aa80ba

Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
journal, March 2001

de Haro, Sebastian; Skenderis, Kostas; Solodukhin, Sergey N.
Communications in Mathematical Physics, Vol. 217, Issue 3
DOI: 10.1007/s002200100381

A Stress Tensor for Anti-de Sitter Gravity
journal, December 1999

Balasubramanian, Vijay; Kraus, Per
Communications in Mathematical Physics, Vol. 208, Issue 2
DOI: 10.1007/s002200050764

Proof of the quantum null energy condition
journal, January 2016

Bousso, Raphael; Fisher, Zachary; Koeller, Jason
Physical Review D, Vol. 93, Issue 2
DOI: 10.1103/PhysRevD.93.024017

Quantum corrections to holographic entanglement entropy
journal, November 2013

Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan
Journal of High Energy Physics, Vol. 2013, Issue 11
DOI: 10.1007/JHEP11(2013)074

Erratum: Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices [Phys. Rev. D 85 , 104049 (2012)]
journal, March 2013

Wall, Aron C.
Physical Review D, Vol. 87, Issue 6
DOI: 10.1103/PhysRevD.87.069904

Proof of a quantum Bousso bound
journal, August 2014

Bousso, Raphael; Casini, Horacio; Fisher, Zachary
Physical Review D, Vol. 90, Issue 4
DOI: 10.1103/PhysRevD.90.044002

Relative entropy equals bulk relative entropy
journal, June 2016

Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan
Journal of High Energy Physics, Vol. 2016, Issue 6
DOI: 10.1007/JHEP06(2016)004

Entropy, extremality, euclidean variations, and the equations of motion
journal, January 2018

Dong, Xi; Lewkowycz, Aitor
Journal of High Energy Physics, Vol. 2018, Issue 1
DOI: 10.1007/JHEP01(2018)081

Gravitation from entanglement in holographic CFTs
journal, March 2014

Faulkner, Thomas; Guica, Monica; Hartman, Thomas
Journal of High Energy Physics, Vol. 2014, Issue 3
DOI: 10.1007/JHEP03(2014)051

Some results on the shape dependence of entanglement and Rényi entropies
journal, February 2015

Allais, Andrea; Mezei, Márk
Physical Review D, Vol. 91, Issue 4
DOI: 10.1103/PhysRevD.91.046002

Dynamics of entanglement entropy from Einstein equation
journal, July 2013

Nozaki, Masahiro; Numasawa, Tokiro; Prudenziati, Andrea
Physical Review D, Vol. 88, Issue 2
DOI: 10.1103/PhysRevD.88.026012

Similar Records in DOE PAGES and OSTI.GOV collections:

Replacing energy by von Neumann entropy in quantum phase transitions

Journal Article Kopp, Angela ; Xun, Jia ; Chakravarty, Sudip - Annals of Physics (New York)

We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.
https://doi.org/10.1016/j.aop.2006.08.002
Von Neumann entropy and phase distribution of two mode parametric amplifier interacting with a single atom

Journal Article Sebawe Abdalla, M ; Obada, A -S.F. ; Abdel-Aty, M - Annals of Physics (New York)

In the present article, we introduce a Hamiltonian model that consists of two modes of the field in a perfect cavity to interact with a single two-level atom. The interaction between the fields has been taken into account and considered to be in the parametric amplifier form. The model in one hand can be regarded as a generalization of the Jaynes-Cummings model (JCM), however, in the other hand it can be considered as a generalization of the parametric amplifier model. Under a certain condition the exact solution to the Schroedinger equation is obtained. Employing this solution and for chosen valuesmore »« less
https://doi.org/10.1016/j.aop.2005.01.002
von Neumann entropy associated with the haldane exclusion statistics

Journal Article Rajagopal, A K - Physical Review Letters; (United States)

We obtain the von Neumann entropy per state of the Haldane exclusion statistics with parameter [ital g] in terms of the mean occupation number [bar n][l brace][ital w]ln[ital w][minus](1+[ital w])ln(1+[ital w])[r brace], where [ital w]=(1[minus][bar n]). This reduces correctly to the well known expressions in the limiting cases of Bose ([ital g]=0) and Fermi ([ital g]=1) statistics. We have derived the second and third order fluctuations in the occupation numbers for arbitrary [ital g]. An elegant general duality relationship between the [ital w] factor associated with the particle and that associated with the hole at the reciprocal [ital g] ismore »« less
https://doi.org/10.1103/PhysRevLett.74.1048
von Neumann entropy of N interacting pencils of radiation

Journal Article Barakat, R ; Brosseau, C - Journal of the Optical Society of America, Part A: Optics and Image Science; (United States)

The von Neumann entropy of N interacting pencils of radiation is analyzed by using their spectral density matrix. When the cross-spectral density is the same for all pairs of pencils, the entropy is evaluated in closed form as a function of Barakat's N-fold polarization measures. Some technical and historical remarks are made concerning the Planck-von Laue entropy of such pencils. 16 refs., 3 figs.
https://doi.org/10.1364/JOSAA.10.000529
The smooth entropy formalism for von Neumann algebras

Journal Article Berta, Mario ; Furrer, Fabian ; Scholz, Volkher B., E-mail: scholz@phys.ethz.ch - Journal of Mathematical Physics

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.
https://doi.org/10.1063/1.4936405

Similar Records

Title: Energy density from second shape variations of the von Neumann entropy

Citation Formats

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime journal, January 2015

Building up spacetime with quantum entanglement journal, June 2010

Entanglement Equilibrium and the Einstein Equation journal, May 2016

Entropy on a null surface for interacting quantum field theories and the Bousso bound journal, April 2015

Building up Space–Time with Quantum Entanglement journal, December 2010

Proof of the generalized second law for rapidly evolving Rindler horizons journal, December 2010

Relative entropy and the Bekenstein bound journal, September 2008

Nonlinear gravity from entanglement in conformal field theories journal, August 2017

Averaged null energy condition from causality journal, July 2017

Gravitational dynamics from entanglement “thermodynamics” journal, April 2014

Saturation of the quantum null energy condition in far-from-equilibrium systems journal, June 2018

Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices journal, May 2012

Cool horizons for entangled black holes journal, August 2013

Holographic proof of the quantum null energy condition journal, July 2016

Shape dependence of entanglement entropy in conformal field theories journal, April 2016

Some calculable contributions to holographic entanglement entropy journal, August 2011

Entanglement density and gravitational thermodynamics journal, May 2015

Local modular Hamiltonians from the quantum null energy condition journal, March 2018

Quantum focusing conjecture journal, March 2016

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence journal, May 2006

Bare Quantum Null Energy Condition journal, February 2018

Modular Hamiltonians on the null plane and the Markov property of the vacuum state journal, August 2017

Thermodynamics of Spacetime: The Einstein Equation of State journal, August 1995

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition journal, September 2016

Lower Bound on the Energy Density in Classical and Quantum Field Theories journal, April 2017

State-dependent divergences in the entanglement entropy journal, October 2016

A covariant holographic entanglement entropy proposal journal, July 2007

Ads/CFT correspondence and symmetry breaking journal, September 1999

Holographic entanglement entropy for general higher derivative gravity journal, January 2014

Violating the quantum focusing conjecture and quantum covariant entropy bound in d ⩾ 5 dimensions journal, August 2017

Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence journal, March 2001

A Stress Tensor for Anti-de Sitter Gravity journal, December 1999

Proof of the quantum null energy condition journal, January 2016

Quantum corrections to holographic entanglement entropy journal, November 2013

Erratum: Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices [Phys. Rev. D 85 , 104049 (2012)] journal, March 2013

Proof of a quantum Bousso bound journal, August 2014

Relative entropy equals bulk relative entropy journal, June 2016

Entropy, extremality, euclidean variations, and the equations of motion journal, January 2018

Gravitation from entanglement in holographic CFTs journal, March 2014

Some results on the shape dependence of entanglement and Rényi entropies journal, February 2015

Dynamics of entanglement entropy from Einstein equation journal, July 2013

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
journal, January 2015

Building up spacetime with quantum entanglement
journal, June 2010

Entanglement Equilibrium and the Einstein Equation
journal, May 2016

Entropy on a null surface for interacting quantum field theories and the Bousso bound
journal, April 2015

Building up Space–Time with Quantum Entanglement
journal, December 2010

Proof of the generalized second law for rapidly evolving Rindler horizons
journal, December 2010

Relative entropy and the Bekenstein bound
journal, September 2008

Nonlinear gravity from entanglement in conformal field theories
journal, August 2017

Averaged null energy condition from causality
journal, July 2017

Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

Saturation of the quantum null energy condition in far-from-equilibrium systems
journal, June 2018

Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
journal, May 2012

Cool horizons for entangled black holes
journal, August 2013

Holographic proof of the quantum null energy condition
journal, July 2016

Shape dependence of entanglement entropy in conformal field theories
journal, April 2016

Some calculable contributions to holographic entanglement entropy
journal, August 2011

Entanglement density and gravitational thermodynamics
journal, May 2015

Local modular Hamiltonians from the quantum null energy condition
journal, March 2018

Quantum focusing conjecture
journal, March 2016

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Bare Quantum Null Energy Condition
journal, February 2018

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
journal, August 2017

Thermodynamics of Spacetime: The Einstein Equation of State
journal, August 1995

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Lower Bound on the Energy Density in Classical and Quantum Field Theories
journal, April 2017

State-dependent divergences in the entanglement entropy
journal, October 2016

A covariant holographic entanglement entropy proposal
journal, July 2007

Ads/CFT correspondence and symmetry breaking
journal, September 1999

Holographic entanglement entropy for general higher derivative gravity
journal, January 2014

Violating the quantum focusing conjecture and quantum covariant entropy bound in d ⩾ 5 dimensions
journal, August 2017

Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
journal, March 2001

A Stress Tensor for Anti-de Sitter Gravity
journal, December 1999

Proof of the quantum null energy condition
journal, January 2016

Quantum corrections to holographic entanglement entropy
journal, November 2013

Erratum: Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices [Phys. Rev. D 85 , 104049 (2012)]
journal, March 2013

Proof of a quantum Bousso bound
journal, August 2014

Relative entropy equals bulk relative entropy
journal, June 2016

Entropy, extremality, euclidean variations, and the equations of motion
journal, January 2018

Gravitation from entanglement in holographic CFTs
journal, March 2014

Some results on the shape dependence of entanglement and Rényi entropies
journal, February 2015

Dynamics of entanglement entropy from Einstein equation
journal, July 2013